Alien calculus and a Schwinger--Dyson equation: two-point function with a nonperturbative mass scale

TL;DR

This paper investigates nonperturbative effects in the massless Wess--Zumino model using alien calculus and Schwinger--Dyson equations, revealing analytic expressions for dominant contributions and challenging triviality arguments.

Contribution

It introduces a novel nonperturbative analysis of the two-point function in the Wess--Zumino model using alien calculus, linking singularities to physical properties.

Findings

Dominant nonperturbative contributions are analytically expressed.

The two-point function shows tame behavior in the deep Euclidean domain.

A nonperturbative singularity appears at the renormalization group invariant scale.

Abstract

Starting from the Schwinger--Dyson equation and the renormalization group equation for the massless Wess--Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep euclidean domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive \(\beta\)-function. On the other side, we have a singularity of the propagator for time like momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.